Question

Would mind tell me what it is limit definition and how to define that?

Answer 1

Here's a pretty good section from Paul Dawkin's Calculus I math notes on the definition of the limit. http://tutorial.math.lamar.edu/Classes/CalcI/DefnOfLimit.aspx

Answer 2

Try solving problems from I.A. Maron, after you've understood about the limits. It's a brilliant, and a challenging book.

Answer 3

we use limits - when we need to find a value for a function at any point we simply use the function.
you must be thinking its obvious. but take an example:
\[(x^{2}-1)\div(x-1)\]
it is a 0/0 form which is not defined in mathematics till yet.
so we take some value \[Deltax\] in the left and right side to determine the value.

limit to exist - you will try to approach the function from left and right side both.
and when the value of the function at that point is equal to left AND right side, function is said to be continuous.

Answer 4

Given a function \[f(x)\] the limit \[\lim_{x \rightarrow a} f(x)\] is the value that the funtion approaches, as 'x' is given values closer and closer to 'a', without actually being 'a'.
How close? Infinitely close.